So why do colliding blocks compute pi?
🛈⏬Solution to the block collision puzzle from last video. Special thanks to these viewers: http://3b1b.co/clacks-thanks Channel support comes from viewers, primarily via https://www.patreon.com/3blue1brown Many of you shared solutions, attempts, and simulations with me this last week. I loved it! Y'all are the best. Here are just two of my favorites. By a channel STEM cell: https://youtu.be/ils7GZqp_iE By Doga Kurkcuoglu: http://bilimneguzellan.net/bouncing-cubes-and-%CF%80-3blue1brown/ NY Times blog post about this problem: https://wordplay.blogs.nytimes.com/2014/03/10/pi/ The original paper by Gregory Galperin: https://www.maths.tcd.ie/~lebed/Galperin.%20Playing%20pool%20with%20pi.pdf I'm not sure if there is an original source fo the solution presented here since it's not the one from the Galperin paper. I found it independently, but certainly not first. I think it's the most natural approach one might take given the problem statement, as corroborated by the fact that one like this is referenced in the NYT wordplay blog linked above, as well as the fact that many solutions people sent my way in this last week had this flavor. If you want to contribute translated subtitles or to help review those that have already been made by others and need approval, you can click the gear icon in the video and go to subtitles/cc, then add subtitles/cc . I really appreciate those who do this, as it helps make the lessons accessible to more people. Music by Vincent Rubinetti. Download the music on Bandcamp: https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown Stream the music on Spotify: https://open.spotify.com/album/1dVyjwS8FBqXhRunaG5W5u ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted on new videos, subscribe: http://3b1b.co/subscribe Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3blue1brown Reddit: https://www.reddit.com/r/3blue1brown Instagram: https://www.instagram.com/3blue1brown_animations/ Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brownHilbert's Curve: Is infinite math useful?
🛈⏬Space filling curves, turning visual information into audio information, and the connection between infinite and finite math (this is a reupload of an older video which had much worse audio). Supplement with more space-filling curve fun: https://youtu.be/RU0wScIj36o For more information on sight-via sound, this paper involving rewiring a ferret's retinas to its auditory cortex is particularly thought-provoking: http://phy.ucsf.edu/~houde/coleman/sur2.pdf Alternatively, here the NYT summary: https://goo.gl/qNuc14 Also, check out this excellent podcast on Human echolocation: https://goo.gl/23f4Yh For anyone curious to read more about the connections between infinite and finite math, consider this Terry Tao blog post: https://goo.gl/NZ4yrW Lion photo by Kevin Pluck Music by Vincent Rubinetti: https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted on new videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3Blue1Brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3Blue1Brownm/r/3Blue1BrownAnna Rudolf Accused of Cheating with an Engine Hidden in her Lip Balm!
🛈⏬Follow me on Instagram for extra content: https://www.instagram.com/agadmator/ Check out the interview with Anna here http://interviews.chessdom.com/anna-rudolf Interview with Christian Bauer here http://interviews.chessdom.com/christian-bauer Report by Marie Boyarchenko here http://reports.chessdom.com/vandoeuvre-open NY Times article here https://www.nytimes.com/2008/01/13/crosswords/chess/13chess.html Christian Bauer vs Anna Rudolf Vandoeuvre Open (2008) Polish Opening: Bugayev Atttack (A00) 1. b4 e5 2. a3 d5 3. Bb2 Nd7 4. e3 Bd6 5. c4 dxc4 6. Bxc4 Ngf6 7. Nf3 O-O 8. Qc2 b6 9. d3 Bb7 10. Nbd2 a6 11. O-O b5 12. Bb3 Rc8 13. d4 exd4 14. exd4 Bd5 15. Bxd5 Nxd5 16. Ne4 N7b6 17. Rad1 c6 18. Nc5 Ra8 19. Rfe1 Qc7 20. g3 h6 21. Nh4 Rfd8 22. Bc1 Bf8 23. Nf5 a5 24. bxa5 Rxa5 25. Qe2 Raa8 26. Qg4 Kh8 27. Qh4 Re8 28. Kg2 Qd8 29. Rxe8 Qxe8 30. Qg4 Nf6 31. Qf3 Nbd5 32. g4 Bxc5 33. dxc5 Qe4 34. h3 Kg8 35. Qxe4 Nxe4 36. Bb2 f6 37. Nd4 Nxc5 38. Nxc6 Nf4+ 39. Kf3 Nfd3 40. Bd4 Rxa3 41. Be3 b4 42. Rb1 b3 43. Nb4 b2 44. Nc2 Rc3 45. Nd4 Kf7 46. Ke2 Na4 47. Kd1 Rc4 48. Ne2 Ke6 49. Kd2 Nb4 50. Kd1 Kd5 51. f3 Na2 52. Bd2 Rc7 53. h4 Kc4 54. Kc2 Nb4+ 55. Kd1 Kb3 56. Nc1+ Rxc1+ 57. Rxc1 bxc1=Q+ 58. Kxc1 Nc3 59. Be3 Ncd5 60. Bd2 Kc4 61. g5 hxg5 62. hxg5 f5 63. Kd1 Kd3 64. Bc1 Nc2 65. Bb2 g6 ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- If you realllly enjoy my content, you're welcome to support me and my channel with a small donation via PayPal, Bitcoin, Litecoin or Nano. Link to PayPal donation https://www.paypal.me/agadmator Bitcoin address 12VEbMQPyLzBoZzw9yuNofph4C9Ansc4iZ Litecoin address LbSuZuBffDCNmr5CSZbY7W2zM83w4ZvnC7 Nano address xrb_383y7ofu5wsyfr9o8rh93aqaq8aixpdcbaud5iubydukz5moiadsirmuzgoq Check out some of the books I enjoy https://www.amazon.com/ideas/amzn1.account.AFWWCIBWCL5PGEPL73FDWK632F7Q/2QAGBMLVXE7MG Check out ALL my videos here https://www.youtube.com/watch?v=fYgd5ZLdHz8&list=PLDnx7w_xuguFTxcfiM11bB1JchtHclEJg Steemit: https://steemit.com/@agadmator/ Facebook: https://www.facebook.com/agadmatoryoutube Twitter: https://twitter.com/agadmator Instagram: https://www.instagram.com/agadmator/ Lichess: https://lichess.org/@/agadmator Chess.com: agadmator League of Legends: agadmator (EUNE, my friend is using my EUWE account for a couple of years now) Blizzard: agadmator #2992 Check out my Hearthstone channel here https://www.youtube.com/channel/UCDKefsd8PMI0FXHwPi5yscg Check out the SUBSCRIBERS VIDEO https://www.youtube.com/watch?v=p-xa0SkpIiA Send your photos and videos here: subscribers.videos.agadmator@gmail.com Send your own games here: subscribers.games.agadmator@gmail.comGödel's Incompleteness Theorem - Numberphile
🛈⏬Marcus du Sautoy discusses Gödel's Incompleteness Theorem More links & stuff in full description below ↓↓↓ Extra Footage Part One: https://youtu.be/mccoBBf0VDM Extra Footage Part Two: https://youtu.be/7DtzChPqUAw Professor du Sautoy is Simonyi Professor for the Public Understanding of Science and a Professor of Mathematics at the University of Oxford. Professor du Sautoy's book as mentioned... In the US it is called The Great Unknown - http://amzn.to/2sfkWpb In the UK it is called What We Cannot Know - http://amzn.to/2r5yztp More of his books: http://amzn.to/2ryEk4r Discuss this one on Brady's subreddit: https://redd.it/6eet91 Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile We are also supported by Science Sandbox, a Simons Foundation initiative dedicated to engaging everyone with the process of science. NUMBERPHILE Website: http://www.numberphile.com/ Numberphile on Facebook: http://www.facebook.com/numberphile Numberphile tweets: https://twitter.com/numberphile Subscribe: http://bit.ly/Numberphile_Sub Videos by Brady Haran Animation in this video by Pete McPartlan Patreon: http://www.patreon.com/numberphile Brady's videos subreddit: http://www.reddit.com/r/BradyHaran/ Brady's latest videos across all channels: http://www.bradyharanblog.com/ Sign up for (occasional) emails: http://eepurl.com/YdjL9What are quaternions, and how do you visualize them? A story of four dimensions.
🛈⏬How to think about this 4d number system in our 3d space. Thanks to supporters: https://www.patreon.com/3blue1brown With extra-special thanks here: http://3b1b.co/quaternion-thanks Quanta article on quaternions: https://www.quantamagazine.org/the-strange-numbers-that-birthed-modern-algebra-20180906/ The math of Alice in Wonderland: https://www.newscientist.com/article/mg20427391-600-alices-adventures-in-algebra-wonderland-solved/ If you want to contribute translated subtitles or to help review those that have already been made by others and need approval, you can click the gear icon in the video and go to subtitles/cc, then add subtitles/cc . I really appreciate those who do this, as it helps make the lessons accessible to more people. Music by Vincent Rubinetti: https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted on new videos, subscribe: http://3b1b.co/subscribe Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3blue1brown Reddit: https://www.reddit.com/r/3blue1brown Instagram: https://www.instagram.com/3blue1brown_animations/ Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brownHow Quantum Mechanics Saved Physics From Ovens
🛈⏬Skillshare is offering SciShow viewers two months of unlimited access to Skillshare for free! https://skl.sh/scishow-11 You might think that quantum physics was discovered because of some super complicated electron behavior or something, but it was actually invented to explain ovens. Hosted by: Hank Green SciShow has a spinoff podcast! It's called SciShow Tangents. Check it out at https://www.scishowtangents.org ---------- Support SciShow by becoming a patron on Patreon: https://www.patreon.com/scishow ---------- Dooblydoo thanks go to the following Patreon supporters: rokoko, Alex Hackman, Andrew Finley Brenan, Lazarus G, Sam Lutfi, D.A. Noe, الخليفي سلطان, Piya Shedden, KatieMarie Magnone, Scott Satovsky Jr, Charles Southerland, Patrick D. Ashmore, charles george, Kevin Bealer, Chris Peters ---------- Looking for SciShow elsewhere on the internet? Facebook: http://www.facebook.com/scishow Twitter: http://www.twitter.com/scishow Tumblr: http://scishow.tumblr.com Instagram: http://instagram.com/thescishow ---------- Sources: http://galileo.phys.virginia.edu/classes/252/black_body_radiation.html http://galileo.phys.virginia.edu/classes/252/PlanckStory.pdf https://chem.libretexts.org/LibreTexts/Howard_University/Howard%3A_Physical_Chemistry_Laboratory/10._Blackbody_Radiation https://www.youtube.com/watch?v=FXfrncRey-4 https://books.google.com/books?id=W5kyppVPyesC&lpg=PP1&pg=PA23#v=onepage&q&f=false https://www.researchgate.net/publication/267650295_A_Brief_History_of_the_T4_Radiation_Law https://www.nobelprize.org/prizes/physics/1911/wien/lecture/ Image Sources: https://en.wikipedia.org/wiki/Max_Planck https://en.wikipedia.org/wiki/File:Einstein_1921_by_F_Schmutzer_-_restoration.jpg https://commons.wikimedia.org/wiki/File:Gustav_Robert_Kirchhoff.jpg https://en.wikipedia.org/wiki/Wilhelm_Wien#/media/File:Wilhelm_Wien_1911.jpg https://en.wikipedia.org/wiki/File:Mplwp_blackbody_nu_planck-wien-rj_5800K.svg https://en.wikipedia.org/wiki/John_William_Strutt,_3rd_Baron_Rayleigh#/media/File:John_William_Strutt.jpgTimes Tables, Mandelbrot and the Heart of Mathematics
🛈⏬The good old times tables lead a very exciting secret life involving the infamous Mandelbrot set, the ubiquitous cardioid and a myriad of hidden beautiful patterns. Time for the Mathologer to go on a serious fact-finding mission. For those of you who’d like to play around a bit with the stunning times table diagrams that we discuss in this video, download the .cdf file http://www.qedcat.com/cardioid.cdf and open it with the free cdf player which you can download from Wolfram Research (the people behind Wolfram Alpha and Mathematica). If you have access to Mathematica you can also open my .cdf file in Mathematica and play with the code. For those of you who are looking for a bit of a challenge, ponder this: 1) Starting with the fact that the nephroid arises from parallel rays being reflected inside a cylindrical coffee cup, try to convince yourself that the 3 times table really does produce the nephroid (some really neat geometry at work here, very similar to the argument for the cardioid that I talk about at the end of the video). (Added 8 November 2015 check out the proof at http://www.qedcat.com/nephroid_proof.pdf ) 2) Why do the diagrams for all the times tables have a horizontal mirror symmetry? 3) Try to explain the pretty patterns corresponding to the 51 and 99 times tables modulo 200 that I display in the video (around the 9:30 mark). 4) (For those of you with a very strong math background) Try to figure out why the cardioid shows up in the Mandelbrot set. The discovery of the stunning patterns that I discuss in this video is due to the mathematician Simon Plouffe. Check out this article http://tinyurl.com/o2hbtsa and his website http://plouffe.fr for other stunning visualisations using modular arithmetic. Quite a few animations have been contributed by various people and linked to in the comments: Here is one of the nicest ones by Mathias Lengler: https://mathiaslengler.github.io/TimesTableWebGL/ Enjoy! Burkard Polster and Giuseppe Geracitano P.S.: The music we are playing at the end is called Shoulder Closure by Gunnar Olsen. It's part of the free YouTube music library. A really nice piece , isn't it?Solving 2D equations using color, a story of winding numbers and composition
🛈⏬An algorithm for numerically solving certain 2d equations. Brought to you by...you! https://patreon.com/3blue1brown Special thanks to these supporters: http://3b1b.co/winding-thanks Even though we described how winding numbers can be used to solve 2d equations at a high level, it's worth pointing out that there are a few details missing for if you wanted to actually implement this. For example, in order to determine how often to sample points, you'd want to have some bounds on the rate at which the direction of the output changes. We will perhaps discuss this more in a follow-on video! Music by Vincent Rubinetti: https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted on new videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3Blue1Brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3Blue1BrownQuantum Gravity and the Hardest Problem in Physics | Space Time
🛈⏬Viewers like you help make PBS (Thank you 😃) . Support your local PBS Member Station here: https://to.pbs.org/DonateSPACE Between them, general relativity and quantum mechanics seem to describe all of observable reality. You can further support us on Patreon at https://www.patreon.com/pbsspacetime Get your own Space Time t­-shirt at http://bit.ly/1QlzoBi Tweet at us! @pbsspacetime Facebook: facebook.com/pbsspacetime Email us! pbsspacetime [at] gmail [dot] com Comment on Reddit: http://www.reddit.com/r/pbsspacetime Help translate our videos! https://www.youtube.com/timedtext_cs_... Previous Episode: How Much Information is in the Universe? https://www.youtube.com/watch?v=XxVlGAFX7vA Hosted by Matt O'Dowd Written by Matt O'Dowd Graphics by Luke Maroldi Assistant Editing and Sound Design by Mike Petrow Made by Kornhaber Brown (www.kornhaberbrown.com) The first few decades of the 20th century was a time of miracles for physics. First, Einstein’s relativity utterly changed the way we think about space, time, motion and gravity. Then the quantum revolution of the 20s and 30s overturned all of our intuitions about the subatomic world. Together, general relativity and quantum mechanics have allowed us to explain nearly every fundamental phenomenon observed, and have predicted many unexpected phenomena that have since been verified. And yet the two theories contradict each other in fundamental ways. In the century since that golden era of physics, we’ve been trying to reconcile the two … without success. But today on space-time I’m going to begin our discussion of the great quest for this union – the quest for a theory of quantum gravity, and for a theory of everything. Special thanks to our Patreon Big Bang, Quasar and Hypernova Supporters: Big Bang Anton Lifshits CoolAsCats David Nicklas Fabrice Eap Quasar Dean Fuqua Mark Rosenthal Mayank M. Mehrota Roman Pinchuk Tambe Barsbay Vinnie Falco Hypernova Brent Mullins Chuck Zegar Donal Botkin Edmund Fokschaner John Hofmann Jordan Young Joseph Salomone Matthew O’Connor Ratfeast Thanks to our Patreon Gamma Ray Burst Supporters: Alexander Rodriguez Alexey Eromenko Benoit Pagé-Guitard Brandon Cook Brandon Labonte Daniel Lyons David Crane Deborah Whittaker Fabian Olesen Greg Allen Greg Weiss James Flowers James Hughes JJ Bagnell Jon Folks Kevin Warne Malte Ubl Mark Vasile Nicholas Rose Nick Virtue Scott Gossett Shannan Catalano سلطان الخليفيA Hole in a Hole in a Hole - Numberphile
🛈⏬Audible: http://www.audible.com/numberphile More links & stuff in full description below ↓↓↓ Cliff's glassware: http://bit.ly/ACME_Klein Extras for this video: https://youtu.be/6Qpfv5y-7WU More videos featuring Cliff Stoll: http://bit.ly/Cliff_Videos Cliff references A Comprehensive Introduction to Differential Geometry by Michael Spivak: http://amzn.to/2cwmdB7 Animation: Pete McPartlan Note from Cliff: Original ideas & suggestions from Peter Nguyen of Coker College and Danny Stoll of U/Chicago Amazing glasswork by Tom Adams, George Chittenden, Lucas Clarke, and Xing Wei Support us on Patreon: http://www.patreon.com/numberphile NUMBERPHILE Website: http://www.numberphile.com/ Numberphile on Facebook: http://www.facebook.com/numberphile Numberphile tweets: https://twitter.com/numberphile Subscribe: http://bit.ly/Numberphile_Sub Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile Videos by Brady Haran Brady's videos subreddit: http://www.reddit.com/r/BradyHaran/ Brady's latest videos across all channels: http://www.bradyharanblog.com/ Sign up for (occasional) emails: http://eepurl.com/YdjL9 Numberphile T-Shirts: https://teespring.com/stores/numberphile Other merchandise: https://store.dftba.com/collections/numberphileDerivative of volume is surface area
🛈⏬In this neat video, I use the Divergence Theorem to show that, in any dimension, the derivative of the volume of a ball of radius r gives you the surface area of the sphere of radius r. So, for instance, it shouldn’t be surprising that (4/3 pi r^3)’ = 4pi r^2. The neat thing is that, at no step do I actually calculate the volume or the surface area. Enjoy!Fermat’s HUGE little theorem, pseudoprimes and Futurama
🛈⏬A LOT of people have heard about Andrew Wiles solving Fermat's last theorem after people trying in vain for over 350 years. Today's video is about Fermat's LITTLE theorem which is at least as pretty as its much more famous bigger brother, which has a super pretty accessible proof and which is of huge practical importance for finding large prime numbers to keep your credit card transactions safe. Featuring a weird way of identifying primes, the mysterious pseudoprimes and lots of Simpsons, Futurama and Halloween references (I love Halloween and so this is a Mathologer video has a bit of a Halloween theme). As usual, thank you very much to Marty and Danil for their help with this video. Enjoy! BurkardWhat does it feel like to invent math?
🛈⏬An exploration of infinite sums, from convergent to divergent, including a brief introduction to the 2-adic metric, all themed on that cycle between discovery and invention in math. Music: Legions (Reverie) by Zoe Keating ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted about new videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: https://goo.gl/WmnCQZ Various social media stuffs: Patreon: https://www.patreon.com/3blue1brown Twitter: https://twitter.com/3Blue1Brown Facebook: https://www.facebook.com/3blue1brown/ Reddit: https://www.reddit.com/r/3Blue1BrownSlay - A Game I've Been Playing For Many Years!
🛈⏬Slay by Sean O'Conner is a strategy game I've been playing for years! Decades even... You can get the game here. http://www.windowsgames.co.uk/slay.html Links! ● Main Channel https://www.youtube.com/user/xisumavoid ● Livestreams http://www.twitch.tv/xisuma (You can see my stream schedule there) ● Discord Server http://discord.gg/xisuma ● Twitter https://twitter.com/xisumavoid ● Facebook http://on.fb.me/xisuma_facebook ● Website http://www.xisumavoid.com ● Patreon https://www.patreon.com/xisumaFractals are typically not self-similar
🛈⏬What fractal dimension is, and how this is the core concept defining what fractals themselves are. Special thanks to the following Patrons: http://3b1b.co/fractals-thanks Patreon page: https://www.patreon.com/3blue1brown Check out Affirm careers here: http://affirmjobs.3b1b.co Music by Vince Rubinetti: https://soundcloud.com/vincerubinetti/riemann-zeta-function One technical note: It's possible to have fractals with an integer dimension. The example to have in mind is some *very* rough curve, which just so happens to achieve roughness level exactly 2. Slightly rough might be around 1.1-dimension; quite rough could be 1.5; but a very rough curve could get up to 2.0 (or more). A classic example of this is the boundary of the Mandelbrot set. The Sierpinski pyramid also has dimension 2 (try computing it!). The proper definition of a fractal, at least as Mandelbrot wrote it, is a shape whose Hausdorff dimension is greater than its topological dimension . Hausdorff dimension is similar to the box-counting one I showed in this video, in some sense counting using balls instead of boxes, and it coincides with box-counting dimension in many cases. But it's more general, at the cost of being a bit harder to describe. Topological dimension is something that's always an integer, wherein (loosely speaking) curve-ish things are 1-dimensional, surface-ish things are two-dimensional, etc. For example, a Koch Curve has topological dimension 1, and Hausdorff dimension 1.262. A rough surfaces might have topological dimension 2, but fractal dimension 2.3. And if a curve with topological dimension 1 has a Hausdorff dimension that *happens* to be exactly 2, or 3, or 4, etc., it would be considered a fractal, even though it's fractal dimension is an integer. ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted about new videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: https://www.youtube.com/playlist?list=PLZHQObOWTQDPHP40bzkb0TKLRPwQGAoC- Various social media stuffs: Twitter: https://twitter.com/3Blue1Brown Facebook: https://www.facebook.com/3blue1brown/ Reddit: https://www.reddit.com/r/3Blue1BrownMusic And Measure Theory
🛈⏬A connection between a classical puzzle about rational numbers and what makes music harmonious.Pi hiding in prime regularities
🛈⏬A story of pi, prime numbers, and complex numbers, and how number theory braids them together. Viewer-supported: https://www.patreon.com/3blue1brown The fact that only primes that are one above a multiple of four can be expressed as the sum of two squares is known as Fermat's theorem on sums of two squares : https://goo.gl/EdhaN2 Special thanks to the following patrons: http://3b1b.co/leibniz-thanks Music by Vince Rubinetti: https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted about new videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3Blue1Brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3Blue1BrownBinary, Hanoi and Sierpinski, part 1
🛈⏬Binary counting can solve the towers of Hanoi puzzle, and if this isn't surprising enough, it can lead to a method for finding a curve that fills Sierpinski's triangle (which I get to in part 2). Thanks to Desmos for their help in supporting this video. They're hiring, and anyone interested should check out https://www.desmos.com/careers Thanks to all Patreon supporters as well, you can support and get early access to future Essence of series here: https://www.patreon.com/3blue1brown I also want to give a special shoutout to the following patrons: CrypticSwarm, Ali Yahya, Dave Nicponski, Juan Batiz-Benet, Yu Jun, Othman Alikhan, Markus Persson, Joseph John Cox, Luc Ritchie, Einar Wikheim Johansen, Rish Kundalia, Achille Brighton, Kirk Werklund, Ripta Pasay, Felipe Diniz, Chris, Curtis Mitchell, Ari Royce, Bright , Myles Buckley, Robert P Zuckett, Andy Petsch, Otavio good, Karthik T, Steve Muench, Viesulas Sliupas, Steffen Persch, Brendan Shah, Andrew Mcnab, Matt Parlmer, Naoki Orai, Dan Davison, Jose Oscar Mur-Miranda, Aidan Boneham, Brent Kennedy, Henry Reich, Sean Bibby, Paul Constantine, Justin Clark, Mohannad Elhamod, Denis, Ben Granger, Jeffrey Herman, Jacob Young.Divergence and curl: The language of Maxwell's equations, fluid flow, and more
🛈⏬Intuitions for divergence and curl, and where they come up in physics. Thoughts on going sponsor-free: https://www.patreon.com/posts/19586800 Special thanks to these supporters: http://3b1b.co/divcurl-thanks My former work on divergence and curl at Khan Academy: https://www.khanacademy.org/math/multivariable-calculus/multivariable-derivatives For more fun fluid-flow illustrations, which heavily influenced how I animated this video, I think you'll really enjoy this site: https://anvaka.github.io/fieldplay/ Music by Vincent Rubinetti: https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted on new videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3blue1brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3blue1brownA Strange Map Projection (Euler Spiral) - Numberphile
🛈⏬Featuring Hannah Fry.... Check out Brilliant (and get 20% off their premium service): https://brilliant.org/numberphile (sponsor) Poster and sticker based on this video: https://teespring.com/en-GB/euler-spiral-world-map More links & stuff in full description below ↓↓↓ More Hannah on Numberphile: http://bit.ly/hannah_vids Hannah's Book (Hello World): https://amzn.to/2Ds1mQg Antipodal Points: https://youtu.be/G2Blr0LycOI The Euler Spiral paper Hannah mentions: https://arxiv.org/pdf/1202.3033.pdf Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile We are also supported by Science Sandbox, a Simons Foundation initiative dedicated to engaging everyone with the process of science. https://www.simonsfoundation.org/outreach/science-sandbox/ And support from Math For America - https://www.mathforamerica.org/ NUMBERPHILE Website: http://www.numberphile.com/ Numberphile on Facebook: http://www.facebook.com/numberphile Numberphile tweets: https://twitter.com/numberphile Subscribe: http://bit.ly/Numberphile_Sub Videos by Brady Haran Animation by Pete McPartlan Patreon: http://www.patreon.com/numberphile Numberphile T-Shirts: https://teespring.com/stores/numberphile Brady's videos subreddit: http://www.reddit.com/r/BradyHaran/ Brady's latest videos across all channels: http://www.bradyharanblog.com/ Sign up for (occasional) emails: http://eepurl.com/YdjL9Who cares about topology? (Inscribed rectangle problem)
🛈⏬An unsolved conjecture, the inscribed square problem, and a clever topological solution to a weaker version of the question, the inscribed rectangle problem (Proof due to H. Vaughan, 1977), that shows how the torus and Mobius strip naturally arise in mathematical ponderings. Patreon: https://www.patreon.com/3blue1brown Special shout out to the following patrons: Dave Nicponski, Juan Batiz-Benet, Loo Yu Jun, Tom, Othman Alikhan, Markus Persson, Joseph John Cox, Achille Brighton, Kirk Werklund, Luc Ritchie, Ripta Pasay, PatrickJMT , Felipe Diniz, Chris, Andrew Mcnab, Matt Parlmer, Naoki Orai, Dan Davison, Jose Oscar Mur-Miranda, Aidan Boneham, Brent Kennedy, Henry Reich, Sean Bibby, Paul Constantine, Justin Clark, Mohannad Elhamod, Denis, Ben Granger, Ali Yahya, Jeffrey Herman, and Jacob Young ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted about new videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: https://www.youtube.com/playlist?list=PLZHQObOWTQDPHP40bzkb0TKLRPwQGAoC- Various social media stuffs: Twitter: https://twitter.com/3Blue1Brown Facebook: https://www.facebook.com/3blue1brown/ Reddit: https://www.reddit.com/r/3Blue1BrownBut WHY is a sphere's surface area four times its shadow?
🛈⏬Two lovely ways of relating a sphere's surface area to a circle. Fourier socks, pi plushies, and more: http://3b1b.co/store Happy holidays! Discuss on reddit: https://www.reddit.com/r/3Blue1Brown/comments/a2gqo0/but_why_is_a_spheres_surface_area_four_times_its/ 3blue1brown is predominantly supported via Patreon: https://www.patreon.com/3blue1brown With special thanks to these members: http://3b1b.co/sphere-thanks The first proof goes back to Greek times, due to Archimedes, who was charmed by the fact that a sphere has 2/3 the volume of a cylinder encompassing it, and 2/3 the surface area as well (if you consider the caps). Check out this video for another beautiful animation of that first proof: https://youtu.be/KZJw0AYn6_k Calculus series: http://3b1b.co/calculus Thanks to these folks for letting me use their images at the end: https://www.youtube.com/user/vlogbrothers https://www.youtube.com/user/physicswoman https://www.youtube.com/user/Vsauce https://www.youtube.com/user/onemeeeliondollars If you want to contribute translated subtitles or to help review those that have already been made by others and need approval, you can click the gear icon in the video and go to subtitles/cc, then add subtitles/cc . I really appreciate those who do this, as it helps make the lessons accessible to more people. Music by Vincent Rubinetti: https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted on new videos, subscribe: http://3b1b.co/subscribe Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3blue1brown Reddit: https://www.reddit.com/r/3blue1brown Instagram: https://www.instagram.com/3blue1brown_animations/ Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brownRiemann Hypothesis - Numberphile
🛈⏬Here is the biggest (?) unsolved problem in maths... The Riemann Hypothesis. More links & stuff in full description below ↓↓↓ Prime Number Theorem: http://youtu.be/l8ezziaEeNE Fermat's Last Theorem: http://youtu.be/qiNcEguuFSA Prof Edward Frenkel's book Love and Math: http://amzn.to/1g6XP6j Professor Frenkel is a mathematics professor at the University of California, Berkeley - http://edwardfrenkel.com The Millennium Prize at the Clay Mathematics Institute: http://www.claymath.org Number Line: http://youtu.be/JmyLeESQWGw CORRECTION: At 7:20 the zeta function of 2 should be (Pi^2)/6 as correctly stated earlier in the video (Basel Problem) Support us on Patreon: http://www.patreon.com/numberphile NUMBERPHILE Website: http://www.numberphile.com/ Numberphile on Facebook: http://www.facebook.com/numberphile Numberphile tweets: https://twitter.com/numberphile Subscribe: http://bit.ly/Numberphile_Sub Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile Videos by Brady Haran Brady's videos subreddit: http://www.reddit.com/r/BradyHaran/ Brady's latest videos across all channels: http://www.bradyharanblog.com/ Sign up for (occasional) emails: http://eepurl.com/YdjL9 Numberphile T-Shirts: https://teespring.com/stores/numberphile Other merchandise: https://store.dftba.com/collections/numberphileThe fix-the-wobbly-table theorem
🛈⏬This video is about the absolutely wonderful wobbly table theorem. A special case of this theorem became well-known in 2014 when Numberphile dedicated a video to it: A wobbling square table can often be fixed by turning it on the spot. Today I'll show you why and to what extent this trick works, not only for square tables but also general rectangular ones. I'll also let you in on the interesting history of this theorem and I'll tell you how a couple of friends and I turned the ingenious heuristic argument for why stabilising-by- turning should work into a proper mathematical theorem. Here is a link to a preprint of the article by Bill Baritompa, Rainer Löwen, Marty Ross and me that I refer to in the video: http://arxiv.org/abs/math/0511490 . This preprint is pretty close to the printed article that appeared in the Mathematial Intelligencer and which lives behind a pay wall, Math. Intell. 29(2), 49-58 (2007). The argument that I show you in this video is somewhat different from the one Bill, Rainer, Marty and I used in our paper. It's a mix of what we do in our paper and the original argument by Miodrag Novacovic as presented by Martin Gardner in his Mathematical Games column. Here is a link to the 2014 Numberphile video on table turning featuring the prominent German mathematician Matthias Kreck http://youtu.be/OuF-WB7mD6k And this is an article by Andre Martin that features an alternative proof for why stabilising-by-turning works for square tables on continuous grounds that are not too steep: http://arxiv.org/abs/math-ph/0510065 Thank you very much to Danil for his Russian subtitles and Marty for his help with getting the draft of the script for this video just right. Enjoy! BurkardImplicit differentiation, what's going on here? | Essence of calculus, chapter 6
🛈⏬Implicit differentiation can feel weird, but what's going on makes much more sense once you view each side of the equation as a two-variable function, f(x, y). Full series: http://3b1b.co/calculus Series like this one are funded largely by the community, through Patreon, where supporters get early access as the series is being produced. http://3b1b.co/support Special thanks to the following Patrons: http://3b1b.co/eoc6-thanks ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted about new videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3Blue1Brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3Blue1BrownThinking visually about higher dimensions
🛈⏬How do you think about a sphere in four dimensions? What about ten dimensions? Podcast! https://www.benbenandblue.com/ Problem-driven learning on at https://brilliant.org/3b1b Special thanks to these patrons: http://3b1b.co/high-d-thanks Check out Ben Eater's channel: https://www.youtube.com/user/eaterbc Music by Vincent Rubinetti: https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted on new videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3Blue1Brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3Blue1BrownProgressive House · Relaxing Focus Music · 24/7 Live Radio
🛈⏬Welcome to our Progressive House & Trance Music live stream! Our live radio will provide you the soundtrack of your day-to-day activities. More music on Spotify: http://bit.ly/TGS-SpotifyPlaylist We're on Discord: https://discord.gg/kqpNgvF For a live stream experience on steroids: https://live.thegrandsound.com Photos by Unsplash: https://unsplash.com ▬▬▬ Bot Commands ▬▬▬ !love ➟ Let everyone know that you 💗 the current track/song. (Also works with !like or !awesome) !track ➟ Shows the name of the currently playing track. (Also works with !song) !google ➜ Shows google results for the currently playing track. !soundcloud ➜ Shows SoundCloud results for the currently playing track. !hug [NAME] ➜ send your friend a hug! !key ➜ Learn the key to success. !inspire ➟ Your daily inspirational quote. !uptime ➟ Shows the time since we started the stream. !tweet ➟ A quick way to tweet about our live stream. !social ➟ Where to find us online. !report [MESSAGE] ➟ Report errors in the live stream to our team. ▬▬▬▬▬▬▬▬▬▬▬▬▬ Genres you'll hear in this live stream: - Progressive House - Progressive Trance - Chill House ● This music works like a charm while studying, working out, or simply chilling with friends. ● Please 'like' this stream if you find it enjoyable, so more people will find it :) ● Missed the name of a track you love? You can seek back up to 4 hours while you are streaming! ● Please communicate in English only so everyone can take part of the conversation. Become a Patreon / Donor: https://www.patreon.com/TheGrandSound Find us online: https://instagram.com/the.grand.sound https://facebook.com/TheGrandSound https://soundcloud.com/TheGrandSound https://thegrandsound.com #ProgressiveHouse #ChillMusic #TheGrandSoundFeynman's Lost Lecture (ft. 3Blue1Brown)
🛈⏬Check out Grant’s channel: 3blue1brown: https://www.youtube.com/3blue1brown This video recounts a lecture by Richard Feynman giving an elementary demonstration of why planets orbit in ellipses. See the excellent book by Judith and David Goodstein, Feynman's lost lecture”, for the full story behind this lecture, and a deeper dive into its content. Tweet referenced at the start: https://twitter.com/3blue1brown/status/1016936129117937664 Music by Nathaniel Schroeder: https://soundcloud.com/drschroeder/elizabeth-the-mouse Music by Vincent Rubinetti: https://soundcloud.com/vincerubinetti/one-two-zeta Support MinutePhysics on Patreon! http://www.patreon.com/minutephysics Link to Patreon Supporters: http://www.minutephysics.com/supporters/ MinutePhysics is on twitter - @minutephysics And facebook - http://facebook.com/minutephysics And Google+ (does anyone use this any more?) - http://bit.ly/qzEwc6 Minute Physics provides an energetic and entertaining view of old and new problems in physics -- all in a minute! Created by Henry ReichI Traded My Tesla For The Model 3 Performance - Regret Buying Mid-Range
🛈⏬I Sold My Tesla Model 3 Mid-Range & Bought A Model 3 Performance! Get 6 Months Free Supercharging - https://ts.la/jason66047 Find Your Next Car - https://www.AutoTempest.com Subscribe for new videos every Wednesday! - https://goo.gl/VZstk7 Recommended Books & Car Products - http://amzn.to/2BrekJm After driving the Tesla Model 3 mid-range, I regretted not opting to upgrade to the Performance AWD Model 3. The Model 3 mid-range features a unique permanent magnet rear motor, which gives it different driving characteristics versus many other electric cars, including the Model S and Model X, which both use induction motors. This video will cover what the differences in the motors are (front and rear), how this affects the driving characteristics of the car, the mechanical differences between the mid-range and Performance, as well as the overall condition that my Tesla Model 3 Performance arrived in. How Do I Know I Didn’t Get Special Treatment From Tesla With Paint Repair/Car Exchange? First off, this seems strange to me, but many have asked if I somehow received special treatment with regards to getting paint fixed, ordering the Tesla, delivery, etc. That’s not how Tesla works, nor myself, but here’s how I know that no special treatment was provided: 1. Both previous videos were filmed before either video was released. I took delivery of the Model 3 Performance BEFORE the video about paint scratches went live. Hence, Tesla had not seen that I had publicly posted paint issues until I already had my new vehicle. The paint video was filmed before I had decided I was going to trade-in the Mid-Range. 2. I specifically selected the vehicle which I bought. I called Tesla to find out what was in inventory, and I selected a red M3P from that inventory, with VIN. Tesla did not choose the new car for me. 3. When I received the Mid-Range with paint scratches, I called Tesla SLC for the fix. I had heard horror stories from friends about the process required to get the paint repaired (multiple body shop visits, coming back worse than before, loss in value from repaint, etc) so I decided against getting the repair and asked Tesla if they could compensate me at all for the damaged paint instead of dealing with the hassle of repair shops. I felt $2,500 was an unjustified payment for the red paint if it arrives defective/scratched. Tesla said they would get back to me about this. They never did before trading in the car. 4. I only put 49 miles on the car before calling Tesla to inform them I wanted to exchange it for the Performance. This was outside of the 3-day return window (we had a bunch of snow after I took delivery, so I waited until snow had melted before driving for the video review, thus no 3-day window). Tesla said they might be able to switch the car due to the special circumstances (71 miles on the odometer, typical 3-day window needs mileage under 500). Then, they told me they could not. How Much Did All Of This Cost? - I bought the Model 3 Mid-Range in November 2018. $46,000 base price. - $2,500 red paint option, $1,500 19” wheel option, and $1,200 delivery. Total: $51,200 - $7,500 tax credit. Actual Total: $43,700 - The trade-in value of the Mid-Range was $43,200. A $500 loss. The $7,500 tax credit can only be applied to the first buyer, so it instantly loses this much in value. Essentially, buying used means getting the tax credit up front. - I bought the Model 3 Performance in December 2018. $64,000 base price. - $2,500 red paint option, and $1,200 for delivery. Total: $67,700 - $7,500 tax credit. Actual Total: $60,200 - Total Cost To Upgrade To Model 3 Performance: $17,000 Don't forget to check out my other pages below! Facebook: http://www.facebook.com/engineeringexplained Official Website: http://www.howdoesacarwork.com Twitter: http://www.twitter.com/jasonfenske13 Instagram: http://www.instagram.com/engineeringexplained Car Throttle: https://www.carthrottle.com/user/engineeringexplained Amazon: https://www.amazon.com/shop/engineeringexplained EE Extra: https://www.youtube.com/channel/UCsrY4q8xGPJQbQ8HPQZn6iA Engineering Explained is a participant in the Amazon Influencer Program. NEW VIDEO EVERY WEDNESDAY!The Brachistochrone, with Steven Strogatz
🛈⏬Steven Strogatz and I talk about a famous historical math problem, a clever solution, and a modern twist. ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted about new videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: https://www.youtube.com/playlist?list=PLZHQObOWTQDPHP40bzkb0TKLRPwQGAoC- Various social media stuffs: Patreon: https://www.patreon.com/3blue1brown Twitter: https://twitter.com/3Blue1Brown Facebook: https://www.facebook.com/3blue1brown/ Reddit: https://www.reddit.com/r/3Blue1BrownTranscendental numbers powered by Cantor's infinities
🛈⏬In today's video the Mathologer sets out to give an introduction to the notoriously hard topic of transcendental numbers that is both in depth and accessible to anybody with a bit of common sense. Find out how Georg Cantor's infinities can be used in a very simple and off the beaten track way to pinpoint a transcendental number and to show that it is really transcendental. Also find out why there are a lot more transcendental numbers than numbers that we usually think of as numbers, and this despite the fact that it is super tough to show the transcendence of any number of interest such as pi or e. Also featuring an animated introduction to countable and uncountable infinities, Joseph Liouville's ocean of zeros constant, and much more. Here is a link to one of Georg Cantor's first papers on his theory of infinite sets. Interestingly it deals with the construction of transcendental numbers! Cantor, Georg (1874), Ueber eine Eigenschaft des Inbegriffes aller reellen algebraischen Zahlen , Journal für die Reine und Angewandte Mathematik, 77: 258–262 http://gdz.sub.uni-goettingen.de/pdfcache/PPN243919689_0077/PPN243919689_0077___LOG_0014.pdf Here is a link to one of the most accessible writeups of proofs that e and pi are transcendental: http://sixthform.info/maths/files/pitrans.pdf Here is the link to the free course on measure theory by my friend Marty Ross who I also like to thank for his help with finetuning this video: http://maths.org.au/index.php/2013/105-events/education-events-2006/316-ice-emamsi-summer-school-2006 (it's the last collection of videos at the bottom of the linked page). Thank you also very much to Danil Dmitriev the official Mathologer translator for Russian for his subtitles. Enjoy! Burkard P.S.: Since somebody asked, I got the t-shirt I wear in this video from here: https://www.zazzle.com.au/polygnomial_t_shirt-235678195975837274 These Zazzle t-shirt are very good quality, but way too expensive (at least for my taste). If you are really keen on one of their t-shirts I recommend waiting for one of their 50% off on t-shirts promotions.Some light quantum mechanics (with minutephysics)
🛈⏬Complementary video on minutephysics: https://youtu.be/zcqZHYo7ONs minutephysics channel: https://www.youtube.com/user/minutephysics Learn more through active problem-solving at Brilliant: https://brilliant.org/3b1b Special thanks to these patrons: http://3b1b.co/light-quantum-thanks Huge thanks to my friend Evan Miyazono, both for encouraging me to do this project, and for helping me understand many things along the way. This is a simple primer for how the math of quantum mechanics, specifically in the context of polarized light, relates to the math of classical waves, specifically classical electromagnetic waves. I will say, if you *do* want to go off and learn the math of quantum mechanics, you just can never have too much linear algebra, so check out the series I did at http://3b1b.co/essence-of-linear-algebra Mistakes: As several astute commenters have pointed out, the force arrow is pointing the wrong way at 2:18. Thanks for the catch! *Note on conventions: Throughout this video, I use a single-headed right arrow to represent the horizontal direction. The standard in quantum mechanics is actually to use double-headed arrows for describing polarization states, while single-headed arrows are typically reserved for the context of spin. What's the difference? Well, using a double-headed arrow to represent the horizontal direction emphasizes that in a quantum mechanical context, there's no distinction between left and right. They each have the same measurable state: horizontal (e.g. they pass through horizontally oriented filters). Once you're in QM, these kets are typically vectors in a more abstract space where vectors are not necessarily spatial directions but instead represent any kind of state. Because of how I chose to motivate things with classical waves, where it makes sense for this arrow to represent a unit vector in the right direction, rather than the more abstract idea of a horizontal state vector, I chose to stick with the single-headed notation throughout, though this runs slightly against convention. Music by Vincent Rubinetti: https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted on new videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3Blue1Brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3Blue1BrownWhy is pi here? And why is it squared? A geometric answer to the Basel problem
🛈⏬A most beautiful proof of the Basel problem, using light. Supported by the community: http://3b1b.co/basel-thanks And by Brilliant: https://brilliant.org/3b1b Brilliant's principles list that I referenced: https://brilliant.org/principles/ Get early access and more through Patreon: https://www.patreon.com/3blue1brown The content here was based on a paper by Johan Wästlund http://www.math.chalmers.se/~wastlund/Cosmic.pdf Check out Mathologer's video on the many cousins of the Pythagorean theorem: https://youtu.be/p-0SOWbzUYI On the topic of Mathologer, he also has a nice video about the Basel problem: https://youtu.be/yPl64xi_ZZA A simple Geogebra to play around with the Inverse Pythagorean Theorem argument shown here. https://ggbm.at/yPExUf7b Some of you may be concerned about the final step here where we said the circle approaches a line. What about all the lighthouses on the far end? Well, a more careful calculation will show that the contributions from those lights become more negligible. In fact, the contributions from almost all lights become negligible. For the ambitious among you, see this paper for full details. If you want to contribute translated subtitles or to help review those that have already been made by others and need approval, you can click the gear icon in the video and go to subtitles/cc, then add subtitles/cc . I really appreciate those who do this, as it helps make the lessons accessible to more people. Music by Vincent Rubinetti: https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted on new videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3Blue1Brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3Blue1BrownWhat does genius look like in math? Where does it come from? (Dandelin spheres)
🛈⏬A beautiful proof of why slicing a cone gives an ellipse. Thoughts on going sponsor-free (for those who missed it): https://www.patreon.com/posts/going-sponsor-19586800 Special thanks: http://3b1b.co/dandelin-thanks New shirts/mugs available: http://3b1b.co/store Video on Feynman's lost lecture: https://youtu.be/xdIjYBtnvZU The 3d animations in the video were done using Grapher, while 2d animations were done using https://github.com/3b1b/manim If you want to contribute translated subtitles or to help review those that have already been made by others and need approval, you can click the gear icon in the video and go to subtitles/cc, then add subtitles/cc . I really appreciate those who do this, as it helps make the lessons accessible to more people. Music by Vincent Rubinetti: https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted on new videos, subscribe: http://3b1b.co/subscribe Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3blue1brown Reddit: https://www.reddit.com/r/3blue1brown Instagram: https://www.instagram.com/3blue1brown_animations/ Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brownThe paradox of the derivative | Essence of calculus, chapter 2
🛈⏬Derivatives center on the idea of change in an instant, but change happens across time while an instant consists of just one moment. How does that work? Check out the Art of Problem Solving: https://aops.com/3blue1brown Note, to illustrate my point for the target audience of a new calculus student, I discussed a hypothetical speedometer that makes distance measurements over a very small time. Interestingly, most actual speedometers in modern cars work by analyzing the induced current of a spinning magnet, which is in some sense the universe implementing the derivative. Full series: http://3b1b.co/calculus Series like this one are funded largely by the community, through Patreon, where supporters get early access as the series is being produced. http://3b1b.co/support Special thanks to the following supporters: http://3b1b.co/eoc2-thanks ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted about new videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3Blue1Brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3Blue1BrownHow pi was almost 6.283185...
🛈⏬Happy pi day! Did you know that in some of his notes, Euler used the symbol pi to represent 6.28..., before the more familiar 3.14... took off as a standard? Plushie creatures now available: http://3b1b.co/store The idea for this video, as well as the live shots, came from Ben Hambrecht, with the writing and animating done by Grant Sanderson. Special thanks to: - University Library Basel, for letting us rummage through their historical collection - Martin Mattmüller from the Bernoulli-Euler center for helpful discussion - Michael Hartl, author of the Tau Manifesto, for pointing us to obscure references - Library of the Institut de France Cinematographer: Eugen Heller Music by Vincent Rubinetti: https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted on new videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3Blue1Brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3Blue1BrownJuggling by Numbers - Numberphile
🛈⏬Juggling with Colin Wright. More links & stuff in full description below ↓↓↓ Colin Wright on Twitter: https://twitter.com/colinthemathmo Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile We are also supported by Science Sandbox, a Simons Foundation initiative dedicated to engaging everyone with the process of science. NUMBERPHILE Website: http://www.numberphile.com/ Numberphile on Facebook: http://www.facebook.com/numberphile Numberphile tweets: https://twitter.com/numberphile Subscribe: http://bit.ly/Numberphile_Sub Videos by Brady Haran Patreon: http://www.patreon.com/numberphile Brady's videos subreddit: http://www.reddit.com/r/BradyHaran/ Brady's latest videos across all channels: http://www.bradyharanblog.com/ Sign up for (occasional) emails: http://eepurl.com/YdjL9 Note from Brady: The occasionally flipped G on the green ball does not mean anything. It's just a result of some image flipping during editing to keep the balls in the right places.The more general uncertainty principle, beyond quantum
🛈⏬The Heisenberg uncertainty principle is just one specific example of a much more general, relatable, non-quantum phenomenon. Apply to work at one of my favorite math education companies: http://aops.com/3b1b Special thanks to the following Patrons: http://3b1b.co/uncertainty-thanks You are the ones making this possible: http://3b1b.co/support For more on quantum mechanical wave functions, I highly recommend this video by udiprod: https://youtu.be/p7bzE1E5PMY Minute physics on special relativity: https://youtu.be/1rLWVZVWfdY Main video on the Fourier transform https://youtu.be/spUNpyF58BY Louis de Broglie thesis: http://aflb.ensmp.fr/LDB-oeuvres/De_Broglie_Kracklauer.pdf More on Doppler radar: Radar basics: https://www.eetimes.com/document.asp?doc_id=1278808 There's a key way in which the description I gave of the trade-off in Doppler radar differs from reality. Since the speed of light is so drastically greater than the speed of things being detected, the Fourier representation for pulse echoes of different objects would almost certainly overlap unless it was played for a very long time. In effect, this is what happens, since one does not send out a single pulse, but a whole bunch of evenly spaced pulses as some pulse repetition frequency (or PRF). This means the Fourier representation of all those pulses together can actually be quite sharp. Assuming a large number of such pulses, it will look like several vertical lines spaced out by the PRF. As long as the pulses are far enough apart that the echoes of multiple objects on the field from different targets don't overlap, it's not a problem for position determinations that the full sequence of pulses occupies such a long duration. However, the trade-off now comes in choosing the right PRF. See the above article for more information. Music by Vincent Rubinetti: https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted on new videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3Blue1Brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3Blue1BrownAbstract vector spaces | Essence of linear algebra, chapter 14
🛈⏬The tools of linear algebra are extremely general, applying not just to the familiar vectors that we picture as arrows in space, but to all sorts of mathematical objects, like functions. This generality is captured with the notion of an abstract vector space. Full series: http://3b1b.co/eola Future series like this are funded by the community, through Patreon, where supporters get early access as the series is being produced. http://3b1b.co/support ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted about new videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: https://goo.gl/WmnCQZ Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3Blue1Brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3Blue1BrownEuler's formula with introductory group theory
🛈⏬How e to the pi i can be made more intuitive with some perspectives from group theory, and why exactly e^(pi i) = -1. Apply to work at Emerald Cloud Lab: - Application software engineer: http://3b1b.co/ecl-app-se - Infrastructure engineer: http://3b1b.co/ecl-infra-se - Lab focused engineer: http://3b1b.co/ecl-lab-se - Scientific computing engineer: http://3b1b.co/ecl-sci-comp Special thanks to the following Patrons: http://3b1b.co/epii-thanks There's a slight mistake at 13:33, where the angle should be arctan(1/2) = 26.565 degrees, not 30 degrees. Arg! If anyone asks, I was just...er...rounding to the nearest 10's. For those looking to read more into group theory, I'm a fan of Keith Conrads expository papers: http://www.math.uconn.edu/~kconrad/blurbs/ ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted about new videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3Blue1Brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3Blue1BrownWhat they won't teach you in calculus
🛈⏬A visual for derivatives which generalizes more nicely to topics beyond calculus. Supported by viewers: https://www.patreon.com/3blue1brown Problem-driven learning by Brilliant: https://brilliant.org/3b1b Essence of calculus series: http://3b1b.co/calculus Special thanks to the following patrons: http://3b1b.co/alt-calc-thanks Music by Vincent Rubinetti: https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted on new videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3blue1brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3blue1brownHow to make a square vortex ring! ft. 3blue1brown
🛈⏬Turbulence with 3blue1brown: https://youtu.be/_UoTTq651dE Dianna from Physics Girl makes DIY crazy vortex ring shapes with Grant Sanderson from 3blue1brown Creator: Dianna Cowern Producer: Dan Walsh Editing: Jabril Ashe Animations: Keegan Larwin, Dan Walsh, Brooke Wimberley, and Jabril Ashe Thanks to Kyle Kitzmiller! http://physicsgirl.org/ http://twitter.com/thephysicsgirl http://facebook.com/thephysicsgirl http://instagram.com/thephysicsgirlTopology Riddles | Infinite Series
🛈⏬Viewers like you help make PBS (Thank you 😃) . Support your local PBS Member Station here: https://to.pbs.org/donateinfi Can you turn your pants inside out without taking your feet off the ground? Start your free trial with Squarespace at http://squarespace.com/infiniteseries and enter offer code “infinite” to get 10% off your first purchase. And check out Vanessa Hill’s documentary Mutant Menu right here! https://www.youtube.com/watch?v=NrDM6Ic2xMM And special thanks to Danny Haymond Jr aka @slothman86 for for his incredible fan art! Tweet at us! @pbsinfinite Facebook: facebook.com/pbsinfinite series Email us! pbsinfiniteseries [at] gmail [dot] com Previous Episode Building an Infinite Bridge https://www.youtube.com/watch?v=1_DOzuaBE84 The Heart of Mathematics https://www.amazon.com/Heart-Mathematics-invitation-effective-thinking/dp/1931914419 Picture Hanging Article:: https://arxiv.org/pdf/1203.3602.pdf Written and Hosted by Kelsey Houston-Edwards Produced by Rusty Ward Graphics by Ray Lux Made by Kornhaber Brown (www.kornhaberbrown.com) Find out why Topology is often called Rubber Sheet Geometry and try to solve these counter-intuitive topological puzzles. Challenge Winners: Alan Chang @Chalkface Comments answered by Kelsey: Louis JX https://www.youtube.com/watch?v=1_DOzuaBE84&lc=z12lu5vx5sepxjemc22mhnualyfajxthv04 Erdmannelchen https://www.youtube.com/watch?v=1_DOzuaBE84&lc=z132hrbbhxbpwvieu231wl3ytxmyznsu0Taylor series | Essence of calculus, chapter 11
🛈⏬Taylor polynomials are incredibly powerful for approximations, and Taylor series can give new ways to express functions. Early access to future series: https://patreon.com/3blue1brown Full series: http://3b1b.co/calculus Series like this one are funded largely by the community, through Patreon, where supporters get early access as the series is being produced. http://3b1b.co/support ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted about new videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3Blue1Brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3Blue1BrownThis Problem STUMPS PhotoMath And Many Solvers! Can You Figure It Out?
🛈⏬Photomath can't solve this, and neither can Mathway, Symbolab, or Desmos. Can you? I explain how you can. A similar problem was given to high school students in Massachusetts, and you really have to know what you're doing to figure it out. Thanks to all patrons! Special thanks this month to: Shrihari Puranik Richard Ohnemus Michael Anvari Kyle This is the only channel to feature math topics suggested by people around the world. Support the channel on Patreon so we can share the beauty of mathematics and make the world a better place: https://www.patreon.com/mindyourdecisions Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Playlist to watch all videos on MindYourDecisions: https://www.youtube.com/playlist?list=UUHnj59g7jezwTy5GeL8EA_g If you buy from the links below I may receive a commission for sales. This has no effect on the price for you. Show your support! Get a mug, a t-shirt, and more at Teespring, the official site for Mind Your Decisions merchandise: https://teespring.com/stores/mind-your-decisions My Books The Joy of Game Theory shows how you can use math to out-think your competition. (rated 4.0/5 stars on 36 reviews) http://amzn.to/1uQvA20 The Irrationality Illusion: How To Make Smart Decisions And Overcome Bias is a handbook that explains the many ways we are biased about decision-making and offers techniques to make smart decisions. (rated 4.6/5 stars on 3 reviews) http://amzn.to/1o3FaAg Math Puzzles Volume 1 features classic brain teasers and riddles with complete solutions for problems in counting, geometry, probability, and game theory. Volume 1 is rated 4.4/5 stars on 13 reviews. http://amzn.to/1GhUUSH Math Puzzles Volume 2 is a sequel book with more great problems. (rated 4.5/5 stars on 6 reviews) http://amzn.to/1NKbyCs Math Puzzles Volume 3 is the third in the series. (rated 4/5 stars on 6 reviews) http://amzn.to/1NKbGlp 40 Paradoxes in Logic, Probability, and Game Theory contains thought-provoking and counter-intuitive results. (rated 4.4/5 stars on 13 reviews) http://amzn.to/1LOCI4U The Best Mental Math Tricks teaches how you can look like a math genius by solving problems in your head (rated 4.8/5 stars on 5 reviews) http://amzn.to/18maAdo Multiply Numbers By Drawing Lines This book is a reference guide for my video that has over 1 million views on a geometric method to multiply numbers. (rated 4.3/5 stars on 6 reviews) http://amzn.to/XRm7M4 Connect with me My Blog: https://mindyourdecisions.com/blog/ Twitter: https://twitter.com/preshtalwalkar Facebook: https://www.facebook.com/pages/Mind-Your-Decisions/168446714965 Pinterest: https://www.pinterest.com/preshtalwalkar/ Tumblr: https://preshtalwalkar.tumblr.com/ Instagram: https://instagram.com/preshtalwalkar/ Patreon: https://www.patreon.com/mindyourdecisions Newsletter (sent only for big news, like a new book release): http://eepurl.com/KvS0rMatrix multiplication as composition | Essence of linear algebra, chapter 4
🛈⏬Multiplying two matrices represents applying one transformation after another. Many facts about matrix multiplication become much clearer once you digest this fact. Full series: http://3b1b.co/eola Future series like this are funded by the community, through Patreon, where supporters get early access as the series is being produced. http://3b1b.co/support ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted about new videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: https://goo.gl/WmnCQZ Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3Blue1Brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3Blue1BrownWhat Is 60÷5(7-5) = ? The Viral Problem Everyone Is Arguing About
🛈⏬What is 60÷5(7-5) = ? Everyone is arguing about this problem, so let's figure out the correct answer! The problem involves the order of operations, historical math notation, and binary expression trees. Glad to see the world is passionate about mathematics! Here is a 1917 article from The American Mathematical Monthly that explains the usage of the division symbol as an exception to the order of operations http://www.jstor.org/stable/2972726?seq=1#page_scan_tab_contents Google evaluation https://www.google.com/#q=60÷5%287−5%29 What is 6÷2(1+2) = ? The Correct Answer Explained https://youtu.be/URcUvFIUIhQ 9 - 3 ÷ 1/3 + 1 = ? The Correct Answer (Viral Problem In Japan) https://youtu.be/07Abat5iBbw Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Playlist to watch all videos on MindYourDecisions: https://www.youtube.com/playlist?list=UUHnj59g7jezwTy5GeL8EA_g This is the only channel to feature math topics suggested by people around the world. Support the channel on Patreon so we can share the beauty of mathematics and make the world a better place: https://www.patreon.com/mindyourdecisions If you buy from the links below I may receive a commission for sales. This has no effect on the price for you. My Books The Joy of Game Theory shows how you can use math to out-think your competition. (rated 3.9/5 stars on 35 reviews) http://amzn.to/1uQvA20 The Irrationality Illusion: How To Make Smart Decisions And Overcome Bias is a handbook that explains the many ways we are biased about decision-making and offers techniques to make smart decisions. (rated 4.6/5 stars on 3 reviews) http://amzn.to/1o3FaAg Math Puzzles Volume 1 features classic brain teasers and riddles with complete solutions for problems in counting, geometry, probability, and game theory. Volume 1 is rated 4.4/5 stars on 13 reviews. http://amzn.to/1GhUUSH Math Puzzles Volume 2 is a sequel book with more great problems. (rated 4.5/5 stars on 6 reviews) http://amzn.to/1NKbyCs Math Puzzles Volume 3 is the third in the series. (rated 4/5 stars on 6 reviews) http://amzn.to/1NKbGlp 40 Paradoxes in Logic, Probability, and Game Theory contains thought-provoking and counter-intuitive results. (rated 4.4/5 stars on 13 reviews) http://amzn.to/1LOCI4U The Best Mental Math Tricks teaches how you can look like a math genius by solving problems in your head (rated 4.8/5 stars on 5 reviews) http://amzn.to/18maAdo Multiply Numbers By Drawing Lines This book is a reference guide for my video that has over 1 million views on a geometric method to multiply numbers. (rated 4.3/5 stars on 6 reviews) http://amzn.to/XRm7M4 Connect with me My Blog: https://mindyourdecisions.com/blog/ Twitter: https://twitter.com/preshtalwalkar Facebook: https://www.facebook.com/pages/Mind-Your-Decisions/168446714965 Google+: https://plus.google.com/108336608566588374147/posts Pinterest: https://www.pinterest.com/preshtalwalkar/ Tumblr: https://preshtalwalkar.tumblr.com/ Instagram: https://instagram.com/preshtalwalkar/ Patreon: https://www.patreon.com/mindyourdecisions Newsletter (sent only for big news, like a new book release): http://eepurl.com/KvS0rThe Mystery of Empty Space
🛈⏬Get ready to re-think your ideas of reality. Join UCSD physicist Kim Griest as he takes you on a fascinating excursion, addressing some of the massive efforts and tantalizing bits of evidence which suggest that what goes on in empty space determines the properties of the three-dimensional existence we know and love, and discusses how that reality may be but the wiggling of strings from other dimensions. Series: Atoms to X-Rays [5/2001] [Science] [Show ID: 5551]Revealing the Nature of Dark Matter
🛈⏬Dr. Dan Hooper, a Theoretical Astrophysicist at Fermilab, explores the current status of the dark matter search and some new thoughts on the nature of this mystery. A signal of gamma rays has been observed from the center of the Milky Way, and it may be the breakthrough that we have long been waiting for. If these gamma-rays are in fact being produced by the interactions of dark matter particles, they promise to reveal much about this elusive substance, and may be a major step toward identifying of the underlying nature of our universe's dark matter.QUILLING DAFFODIL FLOWER TUTORIAL | quilling flor de narciso tutorial
🛈⏬QUILLING DAFFODIL FLOWER TUTORIAL VIDEO Thanks for watching , please like and subscribe my channel!

Sneaky Topology

Solving a discrete math puzzle using topology. Want more fair division math fun? Check out this Mathologer video https://youtu.be/7s-YM-kcKME (Seriously, Mathologer is great) These videos are supported by the community. https://www.patreon.com/3blue1brown The original 1986 by Alon and West with this proof https://m.tau.ac.il/~nogaa/PDFS/Publications/The%20Borsuk-Ulam%20Theorem%20and%20bisection%20of%20necklaces.pdf VSauce on fixed points https://youtu.be/csInNn6pfT4 EE Paper using ideas related to this puzzle https://dl.acm.org/citation.cfm?id=802179 I first came across this paper thanks to Alon Amit's answer on this Quora post https://www.quora.com/As-of-2016-what-do-mathematicians-on-Quora-think-of-the-3Blue1Brown-maths-videos If you want to contribute translated subtitles or to help review those that have already been made by others and need approval, you can click the gear icon in the video and go to subtitles/cc, then `add subtitles/cc`. I really appreciate those who do this, as it helps make the lessons accessible to more people. Music by Vincent Rubinetti: https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted on new videos, subscribe: http://3b1b.co/subscribe Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3blue1brown Reddit: https://www.reddit.com/r/3blue1brown Instagram: https://www.instagram.com/3blue1brown_animations/ Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown